Laid Back Holiday Brunch

Name: Laid-Back Holiday Brunch
Ingredients: 2 cups whole milk; 2 tablespoons Dijon mustard, plus more for serving; 4 tablespoons unsalted butter; 1 large shallot, diced; 1 clove garlic, minced; 3 tablespoons all-purpose flour; 2 1/2 cups grated Gruyere (about 8 ounces); Pinch of ground nutmeg; Kosher salt and freshly cracked black pepper; 4 ounces French ham slices, cut or torn into 1-inch pieces; 1 cup grated Parmesan (about 3 ounces); 2 sprigs thyme; 1 loaf sourdough bread, cut into sandwich slices; Olive oil, for drizzling; Flaky sea salt; 6 large eggs; 1/4 cup half-and-half; Kosher salt; 2 tablespoons unsalted butter; 1 bunch chives, finely chopped; 3 blueberry muffins, cut in half; 3 raspberry danishes, cut in half; 3 pain au chocolat, cut in half; 2 cups assorted fresh fruit of your choice; 1 savory babka, sliced